Go-live for a public integration when every customer uses their own Docusign account

am building a multi-tenant SaaS product and I want to make sure I pick the correct integration type before I promote my integration key.

Setup:
- One integration key, eSignature REST API, Authorization Code Grant, confidential client
- Each customer connects THEIR OWN existing Docusign account via OAuth consent
- Envelopes are created in, sent from, and billed to that customer's account
- No reselling, no billing through my company, no embedded signing ceremony in my UI

What the docs say, as I read them: "private custom integration" is for customers building an app for their own use, while "public integration" is for apps used by multiple Docusign customers and requires Docusign Partner Program membership to go live.

My questions:
1. Does my setup count as a public integration, or does private custom cover it, given that every account involved belongs to the customer and not to me?
2. If it is public, is Partner Program membership enforced at go-live even when there is no reselling and no embedding?
3. If membership is not an option for a company of my size, is there any supported path for this model, or is the answer simply no?

Any pointer to the authoritative doc section would be appreciated.